Early this the season, the Tigers walked A.J. Pierzynski in the top of the sixth with runners on second and third, one out, Detroit losing 3-1, and Carlos Quentin on deck for the White Sox. Justin Verlander was on the mound for the Tigers.

Issuing an intentional walk in that situation is particularly annoying to me. I’m sure I’m not the only one who knows that pitching to a batter with the bases juiced is not easy. In fact, in the AL from 1998 to 2007 with the bases loaded and one out, batters had a .359 wOBA (weighted on-base average), as compared to an overall average wOBA of .343. Compare that to the average wOBA with runners on second and third, and one out: .348

But, whether you think that a particular strategy is annoying or not, or even whether you think it is correct, does not make it so, one way or the other. If that were the case, most of the commentators we see and hear on the radio and TV, as well as many baseball insiders, would be anointed as geniuses, and we, the analysts and sabermetricians, would indeed be just geeks living in our mothers’ basements.

In other words, the only way to figure out whether that intentional walk was “correct” is to do the math. Opinions, experience and annoyances don’t matter. Some things in baseball are obvious. Many things, such as the typical intentional walk, are not.

In The Book: Playing the Percentages in Baseball, co-authored by yours truly, Tom Tango and Andrew Dolphin, we state that, generally, an intentional walk is a poor strategy, other than perhaps with two outs, runners on second and third, and an unprotected elite hitter at the plate. However, The Book also says that a situation with one out, men on second and third, and the pitching team trailing or tied, which is exactly what Leyland and the Tigers were facing, can be an opportunity for a correct free pass. Of course, as is often the case, it all depends on the personnel and the situation.

Let’s look at some data on intentional walks in general. I’m using data from the AL only, to eliminate the “intentional walk of the eighth place hitter to get to the pitcher” (which is a separate analysis), as well as to avoid throwing Barry Bonds into the fray.

From 1998 to 2007, AL teams issued a whopping 4,001 intentional walks. That is an average of more than 28 per team per year. You might think that an overwhelming majority of those were executed in the very late innings, when the intentional walk is more likely to be the correct strategy. In fact, 1,753, or 12.5 per team per year, a little less than half of all intentional walks, were issued in the sixth inning or earlier. Of those, 966 were issued with two outs, 752 with one out, and 35 with no outs. You really have to wonder what was going on that a manager would issue an intentional walk in the sixth inning or earlier with no outs. If you want to know, you’ll have to look it up yourself!

Of those 1,753, 1,196 (68 percent) were issued with the batting team ahead, 161 (9 percent) with the batting team behind, and 397 (23 percent) with the game tied. When the issuing team was trailing, the number of runs behind was pretty much equally spread out among one, two, three and four or more runs. The 161 times the team was ahead, it was by one run 127 times, two runs 30 times, and, somewhat curiously, three runs three times and four runs or more once. You can look those up too, if you want. Maybe there are errors in the data. It is a little hard to believe that any manager would opt to intentionally walk someone with a three-or-more-run lead.

What about with runners on second and third? In that situation, 848 times an intentional walk was issued before the seventh inning. Of those, a majority, 508, were with one out. So, the “Pierzynski intentional walk” happens about 3.6 times per team per year, not such an unusual occurrence.

Because we are looking at the early and mid innings, one through six, we are going to use run expectancy (RE) as a proxy for win expectancy (WE) in our analysis. By that, I mean that while we always want to use WE to evaluate strategy decisions in baseball, if we are dealing with the early and mid innings, whatever answer we get using RE is usually going to be the same answer we would get if we were using WE instead. Not always, but usually. The closer the decision, of course, the more we might find that RE and WE yield different answers, even in the early innings.

Anyway, looking at the RE chart for the AL, 1998-2007, below, we see we have an RE of 1.487 with second and third and one out, and 1.695 with the bases loaded. Of course, that is with league-average batters and pitchers. Presumably, you are walking a well-above-average batter who is also a lot better than the following hitter, and/or the on-deck batter (plus pitcher) is a heck of a double play threat. Still, .208 runs is a lot of cheese to make up. Simply walking the batter to “set up the double play,” which is a common explanation for the intentional walk, is not going to help you reduce the other team’s run scoring potential, since the 1.695 runs that score, on the average, when the bases are loaded already include the GIDP.

So, how many runs were actually scored by the batting team after those 508 intentional walks? Surely, it must be closer to the 1.487 runs that score when a batter comes to the plate with runners on second and third with one out, than the 1.695 runs that score with the bases loaded. Managers must know that the next batter is particularly DP prone, or that the batter/pitcher matchup is particularly favorable to the pitcher, such that 1.695 runs is merely a pipe dream for the batting team, right? Well, the answer turns out to be a nightmare for the manager!

After an intentional walk, 1.722 runs were actually scored. Ouch! That can’t be good. We go from a potential 1.487 runs to an actual 1.722 runs. But, we’re not done with the analysis yet. Maybe, just maybe, the RE before the intentional walk was more than (or at least close to) the 1.722 runs that actually scored. Seems like a stretch, but we’ll see.

First, let’s see what kinds of batters and pitchers are on the field when a typical intentional walk is issued in this situation. As you might expect, when an intentional pass was issued, 82 percent of the time the batter being walked had the platoon advantage. After the walk, the next batter had the platoon advantage only 31 percent of the time. When a batter came up in the same situation and wasn’t issued an intentional walk, he had the platoon advantage 54.6 percent of the time, about average for a hitter, and the next batter had the advantage 58.8 percent of the time.

Because most pitchers are right- handed, batters who were intentionally walked were RH only 39.3 percent of the time, and the next batter was RH 67.3 percent of the time. For batters not intentionally walked, 59.4 percent were RH and 55.3 percent of the next batters were RH.

Take notice, baseball. Few things endure just as they've always been, casual pursuits least of all.

So clearly, managers are paying a lot of attention to the platoon advantage when deciding whom to walk and whom to pitch to. The bottom line: When an intentional walk is issued in this situation (and probably in most situations), the batter tends to have the platoon advantage and the next batter tends not to.

In case you were wondering, the next batter after the intentional walk, the one who comes up with the bases loaded, does tend to be DP prone. His DP rate is about 8 percent higher than the intentionally walked batter, and about 22 percent higher than an average batter. Those two numbers are a little misleading, however, as our “next batters” (after an intentional walk) tend to be right-handed, and middle or bottom-of-the-batting-order guys, so naturally, they tend to be slow and DP prone.

Pitchers who are on the mound when an intentional walk is issued also have a higher GIDP rate than those on the mound when the batter is not intentionally walked, and the average AL pitcher. Their DP rate is 14 percent higher than the average AL pitcher, and 6 percent higher than those pitchers who were on the mound when these same batters were not walked with runners on second and third and one out. So the propensity of the pitcher to induce a GIDP also seems to be a factor in the manager’s thinking process.

Still, even with all these double play balls and platoon advantages (for the pitcher) flying all over the field, the batting team still somehow managed to score 1.722 runs after an intentional walk that loaded the bases, when a random bases-loaded situation scores only 1.695 runs on average.

Since the intentionally walked batter tends to have the platoon advantage and the next batter does not, let’s look at an extreme hypothetical situation where all batters who are intentionally walked are opposite-handed from the pitcher and all on-deck batters are same-handed, but both groups of batters are otherwise league average (or at least equal to the average batter who bats in that situation). Here are the overall RE’s (AL, 1998-2007) with runners on second and third and one out with the batter having the platoon advantage, and with the bases loaded, one out, and the batter not having the platoon advantage:

Second and third, one out, platoon advantage:

1.519, a gain of .032 runs, a fairly sizeable gain.

Bases loaded, no platoon advantage:

1.627, a loss of .068 runs, quite a sizeable loss.

So, even with our “dream” intentional walk situation, the batting team still gains .108 runs, according to the RE tables. And of course, the RE with the bases loaded, our post-IBB situation, is not relevant to the analysis, since we already know that teams score 1.722 runs after the intentional walk. We don’t care how many runs they are supposed to score.

But, we still don’t really know how many runs would have scored had the intentionally walked batter been pitched to. Not only does he tend to have the platoon advantage, but he tends to be a well-above average batter, Mr. Pierzynski not withstanding. Here is how often each batting slot gets intentionally walked in the situation at hand:

As expected, batters in the middle and bottom of the order tend to get intentionally walked. Of course, in the AL, no matter whom you walk, the next batter tends to be similar in talent, at least according to his batting slot. For example, the No. 3 batter gets intentionally walked the third most frequently. But if you walk him, you have to pitch to the cleanup hitter, usually no slouch. Even with the most intentionally walked slot, No. 4, you have to pitch to the fifth batter, generally a pretty good hitter.

You would assume that managers tend to choose their intentional walks carefully in the early innings, such that the following batter happens to be quite a bit worse than the batter being walked. Let’s see if that is true.

The average wOBA for an intentionally walked batter in our situation is .373. That is indeed a very good batter. The average batter is the AL has a .343 wOBA.

What about the next batter? His average wOBA is .361, still a well-above-average batter. Even considering that this batter tends not to have the platoon advantage, it is no wonder that the batting team scores 1.722 runs after the intentional walk. Unfortunately (for the team issuing the walk), there is not a whole lot of separation between the batter being walked and the one on-deck. But these are each group of batters’ overall wOBA. What about if we take into consideration platoon advantage?

According to The Book, the average platoon differential for a right-handed batter is 17 points in wOBA and for a lefty, 27 points. So, adjusted for platoon advantage, our intentionally walked batters hit .380 in wOBA and the next batters hit .357, or a 23-point difference, better than 14 points, but still not earth-shattering.

Now, given that the batter being walked is a very good batter, and tends to have the platoon advantage, such that his expected wOBA is around .380, how can we estimate how many runs would have scored had he been allowed to hit, so that we can compare that to the actual 1.722 runs scored after the intentional walk? Once we do that, our job is done and we can go back home to the wife and kids, satisfied in knowing that we have solved another baseball enigma, and made the world a better place in doing so.

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Great article but I think you have your numbers reversed regarding the game score.

“Of those 1,753, 1,196 (68 percent) were issued with the batting team ahead, 161 (9 percent) with the batting team behind, and 397 (23 percent) with the game tied.”